One type of a conventional FM modulator comprises a ROM (Read Only Memory) for storing amplitude values of a quarter period of a sine wave at addresses based on phases thereof, and a signal processor for controlling the reading of a signal from the ROM. The FM modulator in which a frequency modulation signal is produced in accordance with the processing of digital signals can be applied to a sound source for a musical synthesizer.
A frequency modulation wave of a peak amplitude P is expressed in the equation (1), where the carrier and modulation wave are of a sine curve. EQU e(t)=Psin(.alpha.t+Isin.beta.t) (1)
In the equation (1), e is the instantaneous amplitude of the modulated carrier, .alpha. is the carrier angular frequency in rad/s, I is the modulation index which is the ratio of the peak deviation to the modulating angular frequency, and .beta. is the modulating frequency.
In operation, a phase is calculated at a sampling time t in the signal processor in accordance with the equation (1) so that a stored signal is read from the ROM at an address thereof which corresponds to the calculated phase. Such signals are sequentially read from the ROM to produce a frequency modulation wave.
According to the conventional FM modulator, however, a large capacity of ROM is necessary to be included, when an interval of sampling times t is shortened. In such a case, an external ROM has been added to the signal processor because there is resulted a shortage in the storing capacity for an internal ROM of the signal processor. On the other hand, a general purpose signal processor is not generally adapted to use an external ROM. Therefore, a special purpose signal processor has been adapted in the conventional FM modulator.
Further, a supplemental calculation is performed to decrease a distortion of an output wave between sampled values. A system in which the supplemental calculation is performed is required to include a large scale of a signal processor as a hardware because a high speed summation and multiplication must be made therein.